Duke Mathematical Journal

Commensurability of co-compact three-dimensional hyperbolic groups

A. M. Macbeath

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Article information

Source
Duke Math. J. Volume 50, Number 4 (1983), 1245-1253.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077303499

Mathematical Reviews number (MathSciNet)
MR726327

Zentralblatt MATH identifier
0588.22009

Digital Object Identifier
doi:10.1215/S0012-7094-83-05054-8

Subjects
Primary: 22E40: Discrete subgroups of Lie groups [See also 20Hxx, 32Nxx]
Secondary: 11F06: Structure of modular groups and generalizations; arithmetic groups [See also 20H05, 20H10, 22E40] 53C35: Symmetric spaces [See also 32M15, 57T15] 57N10: Topology of general 3-manifolds [See also 57Mxx] 57S99: None of the above, but in this section

Citation

Macbeath, A. M. Commensurability of co-compact three-dimensional hyperbolic groups. Duke Mathematical Journal 50 (1983), no. 4, 1245--1253. doi:10.1215/S0012-7094-83-05054-8. http://projecteuclid.org/euclid.dmj/1077303499.


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References

  • [1] R. Fricke and F. Klein, Vorlesungen über die Theorie der automorphen Funktionen, Vol. 1, p. 335 ff. (Teubner, Leipzig, 1897, reprint Johnson, New York, 1965).
  • [2] T. Jørgensen, Compact $3$-manifolds of constant negative curvature fibering over the circle, Ann. Math. (2) 106 (1977), no. 1, 61–72.
  • [3] F. Lannér, On complexes with transitive groups of automorphisms, Comm. Sém., Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 11 (1950), 71.
  • [4] A. M. Macbeath, Generators of the linear fractional groups, Number Theory (Proc. Sympos. Pure Math., Vol. XII, Houston, Tex., 1967), Amer. Math. Soc., Providence, R.I., 1969, pp. 14–32.
  • [5] G. D. Mostow, Strong rigidity of locally symmetric spaces, Princeton University Press, Princeton, N.J., 1973.
  • [6] A. Weil, On discrete subgroups of Lie groups, Ann. of Math. (2) 72 (1960), 369–384.

See also

  • See also: A. M. Macbeath. Erratum: “Commensurability of co-compact three-dimensional hyperbolic manifolds,” vol. 50 (1983) pp. 1245–1253. Duke Math. J. Vol. 56, No. 1 (1988), pp. 219–219.